Answer:
48 feet
Explanation:
Let the height of the balloon above the ground be h feet and the time passed be t seconds.
Red balloon
h= 2t +40 -----(1)
• where 40 is its initial height and 2t represents an increase of 2 feet in height for every second that has passed
Blue balloon
h= -3t +60 -----(2)
• where 60 is its initial height and -3t represents the balloon decreasing 3 feet in height for every second that has passed.
When the two balloons are of the same height above the ground, the value of h in both equations are equal. Thus, let's equate (1) and (2) to find the time when both balloons are at the same height above the ground.
2t +40= -3t +60
Bring t terms to one side, constant to the other:
2t +3t= 60 -40
Simplify:
5t= 20
Dividing both sides by 5:
t= 20 ÷5
t= 4
Hence, both balloons are at the same height after 4 seconds.
Substitute t= 4 to any of the two equations to find the height of the balloons.
h= 2t +40 -----(1)
When t=4,
h= 2(4) +40
h= 8 +40
h= 48
The balloons are 48 feet above the ground when they are the same height above the ground.